Vol 463 | 18 February 2010 | doi:10.1038/nature08824
LETTERS
Upside-down differentiation and generation of a
‘primordial’ lower mantle
Cin-Ty A. Lee1, Peter Luffi1, Tobias Höink1, Jie Li2, Rajdeep Dasgupta1 & John Hernlund3
Except for the first 50–100 million years or so of the Earth’s history,
when most of the mantle may have been subjected to melting, the
differentiation of Earth’s silicate mantle has been controlled by
solid-state convection1. As the mantle upwells and decompresses
across its solidus, it partially melts. These low-density melts rise to
the surface and form the continental and oceanic crusts, driving
the differentiation of the silicate part of the Earth. Because many
trace elements, such as heat-producing U, Th and K, as well as the
noble gases, preferentially partition into melts (here referred to as
incompatible elements), melt extraction concentrates these elements into the crust (or atmosphere in the case of noble gases),
where nearly half of the Earth’s budget of these elements now
resides2. In contrast, the upper mantle, as sampled by mid-ocean
ridge basalts, is highly depleted in incompatible elements, suggesting a complementary relationship with the crust. Mass balance
arguments require that the other half of these incompatible elements be hidden in the Earth’s interior. Hypotheses abound for the
origin of this hidden reservoir3–6. The most widely held view has
been that this hidden reservoir represents primordial material
never processed by melting or degassing. Here, we suggest that a
necessary by-product of whole-mantle convection during the
Earth’s first billion years is deep and hot melting, resulting in the
generation of dense liquids that crystallized and sank into the lower
mantle. These sunken lithologies would have ‘primordial’ chemical
signatures despite a non-primordial origin.
The prevailing view of a primordial lower mantle reservoir is driven
largely by the isotopic signatures of noble gases in mid-ocean ridge
basalts (MORBs) and ocean island basalts. MORBs, which tap the upper
mantle, are depleted in primordial noble gas components, whereas
ocean island basalts are enriched (for example, high 3He/4He) and are
therefore thought to indicate the presence of undegassed primitive
reservoirs deep within Earth’s interior7,8. These observations have led
to the paradigm of layered mantle convection for the Earth: that only
the upper 660 km of the mantle has differentiated, whereas the lower
mantle (deeper than 660 km) has remained unprocessed, thus retaining
its primordial and undegassed signatures. However, preservation of a
primordial lower mantle is at odds with seismic evidence that some
slabs descend to the core–mantle boundary, which suggests wholemantle convection9. To reconcile this discrepancy, Fe-rich chemical
boundary layers formed by sinking of Hadean (the first 100 million
years of the Earth’s history) magma ocean liquids or by subduction
of oceanic crust have been suggested as possible alternatives to a
primordial layer1,10–12, but these scenarios are unlikely to preserve primordial noble gas signatures, because any magma that rises to the Earth’s
surface will have degassed.
A very different story would emerge if liquids sink instead of rise.
Under certain high-pressure conditions, it has been suggested that
peridotite partial melts may be more dense than solid peridotite
because such liquids are Fe-rich and more compressible than
solids13–15. Partial melts of peridotite at 9–23 GPa (270–660 km) are
ultramafic (MgO . 25 wt%) and more enriched in Fe than their lowpressure equivalents because Fe is favoured in liquids with increasing
temperature and pressure16. Figure 1a compares the densities of these
melts calculated for a mantle potential temperature of 1,400 uC (representative of modern mantle15,17,18; see Methods) with the presentday mantle density structure as represented by the Preliminary
Reference Earth Model (PREM)19. At pressures greater than 14 GPa
(that is, deeper than the 410 km discontinuity) and less than ,10 GPa
(,300 km), liquids are less dense than PREM and hence rise (these
results are consistent with ref. 20). However, within the upper mantle
(,,410 km) there is a depth interval of #100 km (,10–14 GPa) just
above the transition zone (14–24 GPa; 410–660 km), wherein partial
melts of peridotite are denser than PREM. This density contrast is
probably independent of temperature because the thermal expansion
coefficients of these liquids and peridotite are similar. Of particular
interest is that melts generated within the transition zone (for
example, the 14 and 18 GPa melt compositions in Fig. 1), while
positively buoyant in their source regions, are denser than PREM
in the 10–14 GPa interval. In contrast, near-solidus melts formed at
pressures .22 GPa in the lowermost transition zone and the upper
part of the lower mantle never become negatively buoyant because
residual ferropericlase suppresses the Fe content in the melt (Fig. 1a).
Provided the Earth’s thermal state was sufficient for deep and hot
melting, we envision the region around the upper mantle–transition
zone (UM–TZ) interface (,14 GPa) as a ‘density trap’ (Fig. 2), in
which buoyant melts rising from the transition zone stall and in which
dense melts sinking from the 10–14 GPa interval in the upper mantle
accumulate. We envision the entire interval of dense melt generation
(,10–22 GPa) as the ‘feeding zone’ of dense melts that converge to
the density trap. These accumulated liquids will eventually crystallize,
either by pressure-induced crystallization (for those liquids that sank)
or by cooling as such material is diverted away from upwelling centres
(Fig. 2). This crystallized product manifests itself in the form of
refertilized solid mantle that is richer in Fe and hence denser than
unadulterated peridotitic mantle. This Fe-rich hybrid rock should
then sink into the lower mantle, eventually settling at the core–mantle
boundary to form a Fe-rich chemical boundary layer (Fig. 2).
The minimum potential temperature necessary for generating
negatively buoyant melts is defined by the top of the feeding zone
(,10 GPa) and corresponds to a potential temperature of ,1,800 uC
(Fig. 1b). The maximum permissible potential temperature is determined by the bottom of the feeding zone (,22 GPa) and corresponds
to a potential temperature of ,2,000 uC (as determined from the
temperature of melting at these depths; Fig. 1b). As shown previously
and as outlined in the Methods21,22, the oldest komatiites (3.5 Gyr)
record potential temperatures of ,1,750 uC. If this is representative
1
Department of Earth Science, MS-126, Rice University, 6100 Main Street, Houston, Texas 77005, USA. 2Department of Geological Sciences, University of Michigan, Ann Arbor,
Michigan 48109-1005, USA. 3Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA.
930
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LETTERS
NATURE | Vol 463 | 18 February 2010
3.4
9
3.5
3.6
Density (g cm–3)
3.7
3.8
3.9
4.0
Upper
mantle
TP = 1,400 ºC
11
Density trap
13
15
~410 km
Feeding
zone
Transition zone
P (GPa)
4.1
17
PREM
Dense melts
14 GPa
16 GPa
18 GPa
100% peridotite
Buoyant melts
10 GPa
>22 GPa
19
21
23
~660 km
25
1,000
1,500
2,000
2,500
3,000
150 km
P (GPa)
5
Feeding zone
10
Negatively buoyant liquids
~410 km
Transition
zone
1,800
15
ºC
20
~660 km
25
1,000
1,500
2,000
T (ºC)
2,500
3,000
of global average potential temperatures in the Early Archaean era,
such liquids could have formed before ,3.5 Gyr ago. A more precise
time window for the formation of Fe-rich hybrid lithologies depends
on how long the temperature of the Earth’s mantle resided between
,1,800–2,000 uC, but cannot be constrained as long as uncertainties
in thermal-history models of the Earth23–25 remain large. However,
for at least some window in Earth’s first billion years, melting within
a
Early Archaean
Figure 1 | Conditions for dense melt generation. a, Densities of 10, 14, 16
and 18 GPa near-solidus melts of peridotite, as well as 100% peridotite melt
from ref. 16, calculated along a mantle adiabat corresponding to a 1,400 uC
potential temperature. Also shown are 22 GPa melts20 for reference. The
thick black line represents the density of mantle from PREM19. The
horizontal field outlined in orange is the pressure interval (,10–14 GPa) in
which liquids are denser than PREM. The blue region is the ‘feeding zone’ for
liquids that eventually become denser than PREM between 10 and 14 GPa.
The purple shaded region is a convergence zone (‘density trap’) in which
melts rising from the transition zone stall, and in which melts sinking from
the 10–14 GPa interval in the upper mantle accumulate. b, The temperature
(T) and pressure (P) equilibration of primary komatiitic magmas from the
South African, west Australian and Canadian cratons, calculated using the
approach of ref. 22 (60.2 GPa, 640 uC, 2s). Also shown are the anhydrous
solidus and liquidus of peridotite (red lines)16, and solid mantle adiabats
(straight grey lines) for given potential temperatures. The intersection of
komatiite P–T data defines the mantle adiabat for generation of komatiites.
The blue-shaded region is the P–T field of the feeding zone in a. The
horizontal shaded region is the P-interval in which melts are denser than
PREM.
the transition zone and just above the UM–TZ interface must have
been a by-product of whole-mantle convection and therefore, generation of Fe-rich hybrid layers, as described here, must have occurred.
Long-term sequestration of these Fe-rich lithologies at the base of
the mantle has intriguing geochemical implications. Because incompatible trace elements, including all the volatiles, are partitioned
into the melt phase, transport of these crystallized liquids to the lower
mantle will give rise to a deep-mantle reservoir preserving primordial
relative abundances of incompatible elements. Primordial (U1Th)/
He ratios, for example, will then result in primordial (high) timeintegrated 3He/4He ratios compared to portions of the mantle that
were processed in the shallow mantle and degassed (and hence will
have evolved to low 3He/4He ratios; Fig. 3a). This sequestered component would have primordial time-integrated 143Nd/144Nd,
87
Sr/86Sr and 206Pb/204Pb because both the parent and daughter elements in these isotope systems are also highly incompatible.
Likewise, the high K in this chemical boundary layer would generate
radiogenic 40Ar, accounting for some of the Ar presumed to be missing from the atmosphere and mantle.
These features are reminiscent of the ‘FOZO’-like geochemical
entity, a component in the mantle thought to be ubiquitous in ocean
b
Late Archaean to present
Ridge
Upwelling beneath
ridge or plume
~410 km
Trapped melts
~660 km
Plume
Ocean island basalt
Upper mantle
Transition zone
Lower mantle
Rise of melts toward
the Earth’s surface
Oceanic
lithosphere
Downward percolation
and solidification of melts
Upward percolation
of melts
Solid mantle
Fe-rich layer
FOZO?
Liquid outer core
Liquid outer core
Figure 2 | Melting in the Archaean and modern mantle. a, Early Archaean
hot mantle: melts generated in the transition zone and lowermost upper
mantle (the feeding zone) accumulate in the density trap at the UM–TZ
interface, and upon crystallization, form a dense and refertilized layer. This
layer founders or is entrained into the lower mantle by background solidstate convection, resulting in a Fe-rich chemical boundary layer at the
bottom of the mantle. This layer is enriched in incompatible elements, noble
gases and heat-producing elements. We note that shallower melting
produces low-density liquids (basalts and komatiites), which rise to the
surface. b, Late Archaean to present cool mantle: melting is restricted to
shallow depths where all liquids are buoyant and rise to the surface. Thermal
upwellings will entrain primordial-like material from the chemical boundary
layer into overlying depleted mantle, generating the ‘FOZO’ geochemical
signature seen in ocean island basalts (see Fig. 3).
931
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LETTERS
NATURE | Vol 463 | 18 February 2010
120
m/M0
Evolution of 3He/4He (R/RA)
a 140
100
80
3
2
1
t (Gyr ago)
Figure 3 | Generation of ‘primordial’, undegassed lower mantle.
a, Evolution of 3He/4He (as R/RA, where R is the isotopic ratio of the
reservoir and RA is that of the present-day atmosphere) in the Earth’s silicate
reservoirs. Differentiation of the silicate Earth generates continental crust
and a deep-mantle reservoir, the latter formed by dense liquids generated
during the Earth’s first billion years. He, U and Th are highly incompatible
and enter the liquid. Dense liquids transport He, U and Th quantitatively to
the lower mantle, but differentiation in the uppermost mantle results in
unidirectional loss of He to the atmosphere and partial transport of U to the
crust (90% of crustal U is assumed to recycle back to the mantle). The rate
constants for flow from shallow to deep mantle, shallow mantle to
continental crust, and continental crust to shallow mantle are 0.47, 0.55, and
0.545 per Gyr. Deep Fe-rich mantle reservoir does not return to the upper
mantle. The inset shows mass proportions (relative to the silicate Earth,
m/M0, where m is mass and M0 is the mass of the silicate Earth) of the two
reservoirs as a function of time. b, 3He/4He versus 143Nd/144Nd in epsilon
units (1 part in 104 deviations from chondrite). Shaded or coloured fields are
ocean island (‘hotspot’) basalt fields8, the horizontal black bar is DMM (as
defined by MORB), the open dotted-outline rectangle is Iceland, FOZO (red
arrow) is the hypothesized common component in the mantle source of
ocean island basalts6, and the star is the time-integrated composition of Ferich lithologies generated by sinking liquids. Mixing lines are between DMM
and ‘sunken liquids’, using Nd from ref. 32 for DMM and multiplying the Nd
concentration of the bulk silicate Earth by five for the sunken liquid
(assuming liquids are 20% melts, though the exact value is not critical). Lines
correspond to different concentration ratios R of (He/Nd)sunken liquid versus
(He/Nd)DMM. Tick marks are at 1% intervals (and stop at 30%).
0
Deep
mantle
40
0
Evolution of 3He/4He (R/RA)
4
60
Shallow
mantle
20
b
1
0.8
0.6
0.4
0.2
0
4
3
2
Time (Gyr ago)
1
0
70
30%
Sunken
magmas
60
1%
R=10
50
R=100
FOZO?
R=1
40
30
20
10
Crust
0
–10
–5
0
εNd
5
10
island basalts26. An unresolved, paradoxical feature of FOZO is that it
is enriched in 3He/4He and hence undegassed. Yet, at the same time,
FOZO has a MORB-like or depleted signature in most other radiogenic isotope systems, which suggests processing through the upper
mantle and by implication degassing6,26. This apparent paradox is
exactly what would be expected (Fig. 3b) if the Fe-rich chemical
boundary layer were to mix with any mantle (only small amounts,
,5%, are needed), such as ‘depleted MORB mantle’ (DMM) or its
ancestral analogue, that has been previously depleted and degassed by
shallow mantle processes. Because the He concentration in the chemical
boundary layer is much higher than in the degassed DMM, mixing of
such material into DMM leads to a substantial increase in 3He/4He but
a 0.7
c
4.0
3.5
(Mg,Fe)-perovskite
Mole fraction
0.5
0.4
(Mg,Fe)O
0.3
0.2
0.1
0
0
0.2
0.4
0.6
0.8
Mass fraction of solidified melt
d
0.4
Bulk
0.2
0.1
0
(Mg,Fe)-perovskite
0
0.2
0.4
0.6
0.8
Mass fraction of solidified melt
3.0
2.5
2.0
1.5
0.0
40
1
(Mg,Fe)O
0.3
d[Inρ]×100
d[InνS]/d[InνP]
1.0
0.5
Ca-perovskite
b 0.5
Molar Fe/(Fe+Mg)
4.5
1
Percentage deviation from pyrolite
Mole fraction
0.6
to only slight changes in the other radiogenic isotope systems, such as
Nd/144Nd, 87Sr/86Sr, 206Pb/204Pb and 187Os/188Os (the concentrations
of these elements in DMM and the chemical boundary layer are not very
different; Fig. 3b). This ‘mixture’ inherits both the depleted signature of
DMM and the undegassed signature of the Fe-rich chemical boundary
layer. This is FOZO. Assuming modern-day passive upwelling rates as
a minimum bound for Archaean upwelling rates, we estimate that a
uniformly distributed layer of pure solidified liquid at the core–mantle
boundary would be ,120–240 km thick (Methods). We also estimate
that such a layer could account for 15–30% of the Earth’s budget of
incompatible trace elements.
The volume of dense melt generated between 10–22 GPa and
trapped at the UM–TZ interface would be more than sufficient to
account for the volume (2 6 0.3%) of the two seismologically resolved
and chemically distinct reservoirs in the lowermost mantle beneath the
Pacific Ocean and Africa27. Thus, it is tempting to associate the material
comprising these ‘chemical piles’ with a Fe-rich chemical boundary
143
DMM
0.0
–0.5
–1.0
–1.5
–2.0
–2.5
–3.0
–3.5
–4.0
–4.5
–5.0
40
60
80
P (GPa)
100
d[Inνφ]
d[InνP]
d[InνS]
60
80
P (GPa)
100
932
©2010 Macmillan Publishers Limited. All rights reserved
Figure 4 | Geophysical properties of Fe-rich
chemical boundary layer. The physical
properties of crystallized 14 GPa ultramafic
liquids16 at lower-mantle pressures. a, Phase
proportions in mol.% in the lower mantle as a
function of mass fraction of solidified ultramafic
liquid. (Mg,Fe)O 5 ferropericlase. b, Molar Fe/
(Fe1Mg) in bulk rock and mineral phases in the
lower mantle (see Methods). c, Density of
solidified melt as a function of pressure:
percentage deviation from pyrolite, d[lnr] 3 100.
The ratio of relative deviations in shear and
compressional velocities is d[lnvS]/d[lnvP].
d, Relative percentage deviations in shear
(d[lnvS]), compressional (d[lnvP]) and bulk
sound velocities (d[lnvw]) from pyrolite as a
function of P. Calculations for pyrolite and
crystallized melt in c and d assume 1,627 uC at the
660 km discontinuity. The bounds on the bands
result from different shear moduli used for Caperovskite: high shear moduli29 give higher vS and
vP and lower vw (thinner lines) and lower shear
moduli31 give the opposite trends (thicker lines).
LETTERS
NATURE | Vol 463 | 18 February 2010
layer formed from these trapped liquids. These dense liquids have
lower (Fe1Mg1Ca)/Si ratios and high Fe and Ca contents compared
to their peridotite sources16. In the deep mantle, lithologies having this
composition will have higher Fe (molar Fe/(Fe1Mg) < 0.2), higher
total perovskite (Ca-perovskite and (Mg,Fe)-perovskite), and lower
ferropericlase ((Fe,Mg)O) content than a peridotite composition
(Fig. 4a,b)28 and will thus have distinct physical properties29. For
example, the increased bulk Fe results in a 4% positive density anomaly
(Fig. 4c). We expect Fe-enrichment to decrease shear modulus and
hence shear velocity vS). We also expect average bulk modulus to be
influenced by phase proportions. Mg- and Ca-perovskite both have
higher bulk moduli than ferropericlase, so in the case of compressional
velocity vP, an increase in perovskite mode would counterbalance the
effect of increasing Fe content. Thus, variations in vP and vS could differ
from those associated with thermal anomalies alone27,30. In detail,
however, actual estimates of seismic velocities at lower-mantle conditions are limited by uncertainties in elastic parameters, particularly for
Ca-perovskite, for which there is still debate over the value of its shear
modulus and pressure derivative29,31. Given these uncertainties,
possible ranges relative to peridotitic mantle are given in Fig. 4c and
d: density increases by 4% (d[lnr]), vS decreases by 2–4% (d[lnvS]), and
vP and bulk sound velocity (vw) decrease only slightly (d[lnvP] 5 22%
and d[lnvw ] 5 20.5 to 21%). These calculations will undoubtedly
evolve as our knowledge of elastic parameters at lower mantle conditions improves, but our predicted lithological compositions will not
change much (Fig. 4a, b).
In summary, a necessary by-product of whole-mantle convection in a
hot Archaean Earth is the generation of dense melts, which in turn
generated Fe-rich hybrid layers at the UM–TZ interface. Sinking of these
layers generates a deep mantle component with ‘primordial’ traceelement and noble gas isotopic signatures, providing an elegant explanation for the ubiquitous FOZO geochemical component in the mantle.
However, in terms of major elements, these dense, high-pressure melts
will not preserve the bulk silicate Earth composition. Estimates of the
bulk silicate Earth composition, which are based on shallow-mantle
samples, are thus biased if segregation of high-pressure melts occurred.
Temperatures and pressures were calculated following the approach of ref. 22.
Densities of liquids were calculated using a Birch–Murnaghan equation of state
and parameters given in refs 17 and 18. Densities and elastic properties of
solidified liquid in the lower mantle were calculated from mineral modes (estimated in two ways: minimization of the Gibbs free energy and mass action laws
coupled with stoichiometric assumptions) and elastic properties extrapolated to
elevated temperature and pressure28,29.
Full Methods and any associated references are available in the online version of
the paper at www.nature.com/nature.
Received 2 June 2009; accepted 7 January 2010.
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Acknowledgements The ideas for this paper were conceived at Rice University and
fine-tuned at the 2008 Cooperative Institute for Deep Earth Research workshop at
the Kavli Institute. We thank G. Masters, M. Ishii, M. Manga, M. Jellinek,
B. Romanowicz, T. Plank, H. Gonnermann, L. Stixrude and C. Lithgow-Bertelloni for
discussions and S. Parman for reviews. G. Masters also helped with velocity
calculations. We thank the Packard Foundation and the NSF for support. J. Li also
acknowledges support from the University of Illinois.
Author Contributions C.-T.A.L. planned the paper, performed the modelling and
wrote the paper; P.L. helped with the modelling and interpretation and figures; T.H.
helped with the geodynamic interpretation; J.L. helped with the density modelling
and interpretation; R.D. helped with the petrologic and geochemical
interpretations; and J.H. helped with the geodynamic and mineral physics
interpretations.
Author Information Reprints and permissions information is available at
www.nature.com/reprints. The authors declare no competing financial interests.
Correspondence and requests for materials should be addressed to C.-T.A.L.
([email protected]).
933
©2010 Macmillan Publishers Limited. All rights reserved
doi:10.1038/nature08824
METHODS
Magma thermobarometry. The Earth’s thermal history provides a key constraint
on whether deep melting ever occurred. Parameterized convection models give
qualitative insight23–25. A more direct approach is to estimate the temperatures
and pressures of the mantle source regions giving rise to Archaean (.2.5 Gyr old)
komatiites, ultramafic magmas inferred to be 40–50% partial melts of a dry fertile
mantle source16,33. These estimated melt fractions are much larger than those
generated under modern mid-ocean ridges (6–10%)32,34 and suggest higher temperatures and initial pressures of melting in the Archaean era. Temperatures,
based on the Mg content of the komatiites, indicate melting temperatures of at
least 1,600–1,700 uC (refs 16 and 35), but there are no direct estimates of pressure.
We refine here the temperature estimates and provide constraints on the
depths of melting using a barometer based on melt silica activity21,22.
Temperatures and pressures of melting were calculated for primary magma
compositions inferred by correcting for the effects of low-pressure fractional
crystallization. Extensive details and principles of magma barometry are presented in ref. 22. Visual Basic code for olivine fractionation correction and P–T
calculations are available upon request from C.-T.A.L. or direct download from
the journal website22. In brief, magmas were corrected for olivine fractionation
until a forsterite content (Mg/(Mg1Fe) 3 100) of 91 for olivine was attained. In
most cases, these minimal to no fractionation corrections were necessary because
of the already very primitive nature of these komatiite compositions: that is,
many appear to be near-primary mantle melts. Temperatures and pressures of
equilibration of these primary magmas were then calculated.
We examined Archaean komatiites (.2.5 Gyr old) from the South African
craton, West Australian craton, and Superior province in the Canadian shield
(GEOROC data, http://georoc.mpch-mainz.gwdg.de). This data set includes the
oldest (3.5 Gyr old) komatiites from the Barberton greenstone belt in South
Africa. Assuming anhydrous conditions, komatiite P–T plots show a supersolidus
array extending from 1,500 uC at 1.5 GPa (,45 km) to 1,750 uC at 7 GPa
(,210 km) (Fig. 1). The array is oblique to that of the anhydrous lherzolite solidus
and approximates a possible P–T path of partial melting. Extrapolation of the P–T
trend to depth yields an intersection with the dry solidus at 8 GPa (240 km) and
1,800 uC; this intersection corresponds to a potential temperature of at least
1,700 uC. For higher potential temperatures, the initial depths of melting must
therefore have been greater than ,240 km (Fig. 1). We note that ref. 36 argue that
komatiites were wet, and as a consequence, their liquidus temperatures are
,1,500–1,600 uC, only 200 uC hotter than the MORB source and within error
of modern hotspot source regions like Hawaii. However, very low ferric to ferrous
iron ratios in komatiite melt inclusions suggest that komatiites were dry33. In any
case, water increases silica activity so that accounting for water decreases calculated temperatures and increases pressures (water depresses the solidus; see ref. 22
for discussion), so our pressures are minimum bounds.
Density calculations for liquids and solids in the upper mantle. Densities of
liquids at increased temperature and pressure (up to 24 GPa) were calculated by
first integrating with respect to temperature at a constant reference pressure P0
(1 bar) and then integrating with respect to pressure at the elevated temperature
T of interest. We followed the procedures of refs 15 and 37. The temperature
integration followed:
ðT
rðT0 ,P0 Þ
ln
~
aðT ÞdT
ð1Þ
rðT ,P0 Þ
T0
where T0 is the reference temperature (298.15 K for solids, but for a liquid, it is
typically some temperature at which the liquid density was experimentally determined), r is density (kg m23), and a is the thermal expansivity (uC21). We used
the following form of the thermal expansivity:
a~a0 za1 T za2 T {1 za3 T {2
ð2Þ
where the ai are constants. After the density at elevated temperature was calculated, the density at elevated pressure was calculated using the third-order Birch–
Murnaghan equation of state:
( " #)
5=3 )(
3
r 7=3
r
3
r 2=3
P~ KT
1{ ð4{K 0 Þ
{
{1
ð3Þ
2
r0
r0
4
r0
where P is pressure (GPa), KT is the isothermal bulk modulus (GPa) at the
temperature of interest, K9 is the pressure-derivative (GPa/GPa) of the bulk
modulus (assumed to be relatively temperature-independent), and
r0 ~r(T,P0 ) is the reference pressure at the temperature of interest. The isothermal bulk modulus KT at the temperature of interest is:
ðT
KT ðT Þ
~{
ln
a(T )dT dT
ð4Þ
KT ðT0 Þ
T0
where dT is assumed to be a dimensionless constant that expresses the temperature
dependency of elastic moduli. We assume that dT <K 0 . Density at elevated pressure
and temperature was then calculated by iteratively solving equations (1) to (4).
Densities of liquids at the reference temperature Tref and 1 bar, r0 ~r(T0 ,P0 ),
for different compositions were calculated using the formulations of ref. 17:
X
V (Tr )~
Xi (T )Vi (Tr )zXNa2 O XTiO2 V Na2 O-TiO2
ð5Þ
where Xi is the oxide mole fraction, Vi (Tr ) is the molar volume of each oxide
species at Tref, and V Na2 O-TiO2 is an effective molar volume for the Na2O–TiO2
interaction (see ref. 17 for parameter values). Liquid densities at elevated pressures
were calculated using equation (3). Isothermal bulk moduli KT and the pressure
derivative K9 were taken from refs 18 and 38. Following these18,38, we adopted a
maximum K9 of 5. Liquid densities were calculated for peridotite partial melts
(from solidus melts to liquidus melts) from the KLB-1 melting experiments of ref.
16. We applied our calculation methods to the liquid compositions of refs 18 and
38 and reproduced their results exactly, verifying the accuracy of our program. All
of the above calculations were done in Visual Basic Excel (coded by C.-T.A.L.).
The macro programs are available from C.-T.A.L. on request.
We did not consider the effects of water on density because high melt fractions
are expected in these high-pressure melts, so water contents of the melt would be
low; in addition, recent studies show that even in the presence of moderate
amounts of water (,2 wt%), liquids still remain negatively buoyant39,40.
Estimating total mass of ‘sunken liquids’. This section concerns how much of
this material may have formed and how much of the Earth’s geochemical budget
resides in this chemical boundary layer. Assuming whole-mantle convection, the
present-day mass flow associated with passive upwelling (for example, the response to subduction) through the transition zone is 1.3 3 1024 kg per Gyr
(assuming 10 cm yr21 for full ridge spreading rate, 40,000 km total ridge length,
,100 km for the average thickness of subducting oceanic lithosphere, and a
mantle density of 3,350 kg m23). This flow rate is a minimum bound because
upwelling rates were probably higher in the Archaean era. Assuming that
Archaean upwelling mantle melted by 10–20% above or within the transition
zone and that such upwelling took place over the Earth’s first billion years, at
least (1.3–2.6) 3 1023 kg of melt could have formed and sunk without ever reaching the Earth’s surface. Spread uniformly around the core–mantle boundary, this
would correspond to a layer ,120–240 km thick. If, as seems likely, the Fe-rich
liquids are mixed in with peridotite before accumulating at the bottom of the
mantle, the effective thickness of this chemical boundary layer will be greater.
The proportion of the Earth’s incompatible trace element budget that could
have been sequestered in this manner is then estimated from the concentration in
the sunken liquid, which we take to be elevated by a factor of 1/f, where f is the
melting degree. If f < 10–20% (using a lower f would increase concentrations),
the integrated mass of sunken liquids could make up 15–30% of the Earth’s
budget of incompatible trace elements. This number could be smaller if the
window of time for generating negatively buoyant liquids is less than a billion
years or larger if background upwelling rates were higher than assumed here. Our
proposed Fe-rich chemical boundary layer has the geochemical characteristics of
an undegassed and primordial mantle despite an origin by partial melting during
whole-mantle convection and thus can solve many of the problems in mantle
geochemistry.
Seismic velocities and densities of lower-mantle mixtures. Densities and seismic
velocities at lower-mantle pressures were calculated following the approach of ref. 29
with a Fortran code written by G. Masters. Phase equilibria were calculated by
assuming that the dominant cations are Ca, Mg, Fe and Si. Then, mole per cent
Ca-perovskite (CaSiO3) equals mole per cent Ca, (Mg,Fe)-perovskite, which equals
the amount of Si not bound up in Ca-perovskite, and ferropericlase makes up the
remaining phase. Mg and Fe are distributed between (Mg,Fe)-perovskite and
Fe=Mg
ferropericlase according to an equilibrium constant KD
5 (Fe/Mg)perovskite/
(Fe/Mg)ferropericlase between perovskite and ferropericlase of 0.25, from ref. 28. We
ignored the effects of T and P on KD. We also ignored the effect of Al in stabilizing
Fe=Mg
(Mg,Fe)-perovskite because the amount of Al is small. The effect of Al on the KD
,
however, could result in KD approaching 1, such that the Fe/(Fe 1 Mg) ratio in Mgperovskite and ferropericlase are the same. Accounting for Al, T and P could change
our results slightly, but given the uncertainties in most of the elastic constants as well
as in how KD varies with Al, T and P, the first-order results presented here using a
constant KD are probably robust.
Isotropic adiabatic bulk and shear moduli (KS and G) were determined from
third-order expressions of the Eulerian finite strain. These calculations required
input values of the molar volume, isothermal bulk and shear moduli, their
pressure derivatives, the Debye temperature, the first and second logarithmic
volume derivatives of the Debye temperature, and the shear strain derivative of
the first derivative of the Debye temperature. These quantities were taken from
ref. 29. For Ca-perovskite, we explored two parameter sets for shear modulus and
©2010 Macmillan Publishers Limited. All rights reserved
doi:10.1038/nature08824
its pressure derivative, one from ref. 29 and the other from ref. 31. Linear mixing
between the elastic moduli and molar volumes of endmember compositions was
assumed (for example, MgO, FeO, MgSiO3, FeSiO3). The density and velocities
of the aggregate lithology are determined by Voigt–Reuss–Hill averaging, using
the phase proportions calculated above.
We calculated velocities and phase equilibria for pyrolite and solidified melt
corresponding to an adiabat that intersects the 660 km discontinuity at 1,900 K.
Because we are examining the simplified (Ca, Mg, Fe, Si) system we do not
compare our calculations directly to PREM. We are primarily interested in the
relative changes in seismic parameters caused by adding solidified melts to
pyrolite. Therefore, in Fig. 4 of the main text, velocity perturbations are given
with respect to our own calculations of simplified pyrolite (our pyrolite calculations are within 1% of PREM). We find the following systematics. Increasing net
Fe content should substantially increase net density, but decrease net seismic
velocities because perovskite and ferropericlase G decrease with increasing Fe/
(Fe1Mg). Adding Si increases the proportion of perovskite phases, resulting in a
slight decrease in net density and an increase in velocities. Because the addition of
melt results in a net increase in Fe but an increase in perovskite proportion
(balanced by a decrease in ferropericlase proportion), our calculations show
that density increases substantially (controlled primarily by Fe), shear velocity
decreases substantially (controlled primarily by Fe), and compressional and bulk
sound velocities decrease only slightly (the latter are controlled by the perovskite/
ferropericlase mode). The perturbations of shear, compressional and bulk sound
velocities should be slightly decoupled from that expected from temperature
variations or bulk Fe-content variations alone. However, we note that depending
on the choice of shear moduli for Ca-perovskite, our results will be slightly
different. Using the parameters of ref. 31, we find that the presence of Caperovskite does not affect shear velocity; consequently shear velocity of the
solidified melt remains low due to the high bulk Fe content. If we use the
parameters of ref. 29, which gives a higher shear modulus and pressure derivative
for Ca-perovskite, the decrease in shear-wave velocity is less pronounced (and at
lowermost mantle pressures, shear velocity actually increases beyond that of the
pyrolitic mantle). Given that the elastic parameters for Ca-perovskite are still
debated, it is probably not worth dwelling on these differences.
We emphasize that these velocity calculations are only as good as the elastic
parameters adopted. Because these elastic parameters at lower mantle conditions
are still a subject of debate, the details of our calculations could change. For
example, if we were to adopt the higher shear modulus and pressure-derivative of
Ca-perovskite29, the shear-wave velocity of the solidified melt would increase
rapidly with depth, resulting in less of a shear-wave velocity anomaly and giving a
low d[lnVS]/d[lnVP] of ,1.
Finally, calculations were also done for a more natural composition (that is,
accounting for additional components, such as Al, Na and K) using Perplex, a
Gibbs free energy minimization program that solves for phase proportions and
compositions given a bulk composition and then calculates seismic velocities
using procedures similar to those described above41. This program incorporates
the thermodynamic and physical properties of lower-mantle minerals from ref.
29. These results were consistent with the simplified oxide system taken above.
33. Berry, A. J., Danyushevsky, L. V., O’Neill, H. S. C., Newville, M. & Sutton, S. R.
Oxidation state of iron in komatiitic melt inclusions indicates hot Archaean
mantle. Nature 455, 960–964 (2008).
34. Langmuir, C., Klein, E. M. & Plank, T. (eds) Petrological Systematics of Mid-Ocean
Ridge Basalts: Constraints on Melt Generation Beneath Ocean Ridges (American
Geophysical Union, 1992).
35. Arndt, N. T. Komatiites, kimberlites and boninites. J. Geophys. Res. 108,
doi:10.1029/2002JB002157 (2003).
36. Grove, T. L. & Parman, S. W. Thermal evolution of the Earth as recorded by
komatiites. Earth Planet. Sci. Lett. 219, 173–187 (2004).
37. Bina, C. R. & Helffrich, G. R. Calculation of elastic properties from thermodynamic
equation of state principles. Annu. Rev. Earth Planet. Sci. 20, 527–552 (1992).
38. Ohtani, E., Kawabe, I., Moriyama, J. & Nagata, Y. Partitioning of elements between
majorite garnet and melt implications for petrogenesis of komatiite. Contrib.
Mineral. Petrol. 103, 263–269 (1989).
39. Sakamaki, T., Suzuki, A. & Ohtani, E. Stability of hydrous melt at the base of the
Earth’s upper mantle. Nature 439, 192–194 (2006).
40. Agee, C. B. Static compression of hydrous silicate melt and the effect of water on
planetary differentiation. Earth Planet. Sci. Lett. 265, 641–654 (2008).
41. Connolly, J. A. D. & Petrini, K. An automated strategy for calculation of phase
diagram sections and retrieval of rock properties as a function of physical
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